(**************************************
 ** FLOAT_INTERVAL.sml
 ** sml
 **
 ** Aleksandar Nanevski
 **
 ** Arithmetic over intervals with
 ** floating point bounds.  When the 
 ** predicates return false, it may 
 ** be because the arguments were NaN.
 **************************************)


signature FLOAT_INTERVAL =
sig
    structure R : REAL

    type interval
    type t = interval

    (* arithmetic *)

    val zero : interval
    val one : interval

    val + : interval * interval -> interval
    val - : interval * interval -> interval
    val * : interval * interval -> interval
    val / : interval * interval -> interval
    val ~ : interval -> interval
    val inv : interval -> interval
    val scale : real * interval -> interval


    (* partial ordering (pairwise) *)
    
    exception Unordered

    val == : interval * interval -> bool
    val < : interval * interval -> bool
    val > : interval * interval -> bool
    val <= : interval * interval -> bool
    val >= : interval * interval -> bool
    val != : interval * interval -> bool
    val sign : interval -> int
    val sup : interval * interval -> interval
    val inf : interval * interval -> interval
    val compare : interval * interval -> order



    (* set operations *)

    val << : interval * interval -> bool
    val >> : interval * interval -> bool
    val member : real * interval -> bool
    val singleton : interval -> bool
    val subset : interval * interval -> bool
    val disjoint : interval * interval -> bool
    val meet : interval * interval -> interval
    val join : interval * interval -> interval



    (* threading (direct image, map) of abs over *)
    (* the interval                              *)

    val threadAbs : interval -> interval

	
    (* coercions *)

    val fromNumber : real -> interval
    val fromBounds : {lo:real, hi:real} -> interval

    (* assumes err is positive, so it never checks for it *)
    val fromMidErr : {mid:real, err:real} -> interval

    val toBounds : interval -> {lo:real, hi:real}
    val toString : interval -> string
    val toNumber : interval -> real


    (* signature-specific functions *)

    (* lower and upper bounds on the size of the interval *)
    val width : interval -> {lo:real, hi:real}

    (* lower and upper bounds on the distance of two intervals *)
    val distance : interval * interval -> {lo:real, hi:real}

    (* distance from [0, 0]; can be computed exactly *)
    val abs : interval -> real

    val isNan : interval -> bool
    val isFinite : interval -> bool

end